Question

The velocity of a body moving in a vertical circle of radius $r$ is $\sqrt{7 g r}$ at the lowest point of the circle. What is the ratio of maximum and minimum tension ?

• A. 4 : 1
• B. $\sqrt{7}: 1$
• C. 3 : 1
• D. 2 : 1

Answer 1

Answer: (A)

Tension is maximum at the lowest point and minimum at the highest point. Tension at the lowest point,
$T_{L}=m g+\frac{m v_{L}^{2}}{r}=m g+\frac{7 m g r}{r}=8 m g \left(\because v_{L}=\sqrt{7 g r}\right)$
Tension at the highest point,
$T_{H} =\frac{m v_{H}^{2}}{r}-m g=\frac{m\left(v_{L}^{2}-4 g r\right)}{r}-m g\left(\therefore v_{L}^{2}-v_{H}^{2}=4 g r\right) $
$=\frac{m(7 g r-4 g r)}{r}-m g=3 m g-m g=2 m g$
$\therefore \frac{T_{L}}{T_{H}}=\frac{4}{1}$ or
$\frac{T_{\max }}{T_{\min }}=\frac{4}{1}$